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Simplify (a/c) sin 2C + (c/a) sin 2A type expressions using the sine rule

This type of question, asked 2 times: 14 May 2024 S1, 26 Apr 2025 S2. All 2 questions below, oldest first.

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  1. Question 1

    14 May 2024 S1

    123
    If the angles A,BA,B and CC of a triangle are in an Arithmetic Progression and if a,ba,b and cc denote the lengths of the sides opposite to A,BA,B and CC respectively, then the value of the expression acsin⁡2C+casin⁡2A\dfrac{a}{c}\sin2C+\dfrac{c}{a}\sin2A is:

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  2. Question 2

    26 Apr 2025 S2

    122
    If the angles A,BA,B and C of a triangle are in A.P. and if a,ba,b and cc denote the length of the sides opposite to A,BA,B and C respectively, then the value of absin⁡2B+basin⁡2A\frac{a}{b}\sin 2B+\frac{b}{a}\sin 2A is

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